Field-theoretic model for dynamics of active Brownian particles

Abstract

We present here, a procedure for developing the hydrodynamic description of a system of active particles starting from microscopic equations of motion. The microscopic dynamics of an individual active particle is described as a Brownian motion having a noise term and momentum dependent frictional coefficients describing the surrounding drag. The single particle dynamics is first used to obtain balance equations for corresponding collective densities. We average the time evolution equation for collective densities over local equilibrium distribution to obtain the hydrodynamic equations in terms of coarse-grained density fields. The macroscopic equation obtained contains multiplicative noise originating from the additive noise in the equation of motion for the active Brownian particle. The parameters of the macroscopic equations are obtained in terms of the microscopic description of the active Brownian system.